Sensitivity check

[yanmin]

I constructed a Multilevel Regression and Synthetic Poststratification model. The model is as follows,

\begin{aligned} &\Pr(y=1) = \mathrm{logit}^{-1}(\mathtt{predictor}) \\ &\mathtt{predictor} = \begin{aligned}[t] &\alpha + \beta_{\mathtt{province}} + \gamma_{\mathtt{age}} + \delta_{\mathtt{gender}} + \epsilon_{\mathtt{urban}} \\ &+ \mathtt{income[province]} \cdot \psi + \mathtt{edu[province]} \cdot \eta + \zeta_{\mathtt{area[province]}} \end{aligned} \\ &\begin{cases} \alpha, \psi, \eta \sim \mathcal{N}(0, 2) \\ \beta \sim \mathcal{N}(0, \sigma_\beta) \\ \gamma \sim \mathcal{N}(0, \sigma_\gamma) \\ \delta \sim \mathcal{N}(0, \sigma_\delta) \\ \epsilon \sim \mathcal{N}(0, \sigma_\epsilon) \\ \zeta \sim \mathcal{N}(0, \sigma_\zeta) \\ \sum \delta \sim \mathcal{N}(0, 0.001) \\ \sum \epsilon \sim \mathcal{N}(0, 0.001) \\ \sigma_\beta, \sigma_\gamma, \sigma_\delta, \sigma_\epsilon, \sigma_\zeta \sim \mathcal{N}(0, 1) \end{cases} \end{aligned}

I would like to perform a sensitivity check to priors. Is there some good advice?
Thanks in advance.

[Bob_Carpenter]

We have a new sum-to-zero vector that should be better than that normal hack for \delta, \epsilon.

The easiest thing to do is to just try different priors and see what they do to quantities of interest in the fit. Here, you have standard normal priors on the \sigma_? and a scale-2 prior on \alpha,\psi,\eta.

[mitzimorris]

If you go through the examples in this repo: Draft Reports | [“Diagnostic Tests”], you will find models and rscripts used to make this plot:

Fig. 2 shows how these hyperprior parameters 𝜏𝛾 and 𝜏𝛿 affect inferences for the prevalence 𝜋. The posterior median of 𝜋 is not sensitive to the scales of the hyperpriors, but the uncertainty in that estimate [is sensitive]. …

[yanmin]

thanks very much